Tire health monitoring systems and methods thereto

ABSTRACT

The disclosed technology includes a system comprising a tire-mounted inertial measurement unit (IMU). The IMU can be configured to measure linear acceleration data and angular velocity data associated with a tire, and the system can be configured to determine various indicators of tire health based on the linear acceleration data and angular velocity data. The system can be configured to determine a distance between the IMU and an outer rolling surface of the tire. The system can be configured to monitor changes in this distance over time, which can be indicative of tread wear over time. Accordingly, the system can be configured to monitor change in the tread depth over time such that the system is configured to monitor tread depth of the tire.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 62/795,363, filed on Jan. 22, 2019, which is incorporated herein byreference in its entirety as if fully set forth below.

BACKGROUND

Driving on worn, low-tread, and low-pressure tires can create a safetyhazard for the driver and passengers of a vehicle, as well as others whomay encounter a vehicle traveling on worn, low-tread tires. For example,a vehicle traveling on worn, low-tread, and/or low-pressure tires may beunable to stop suddenly and efficiently while traveling on roads duringinclement weather, such as rain, snow, ice, or mud. This can result in acollision involving the vehicle that could have been otherwise avoided,and such collisions can cause property damage and/or personal injury.

Tire treads are designed to maintain solid contact and grip on the roadeven during inclement weather. Driving on tires with insufficient treads(i.e., balding or low-tread tires) can provide an increased risk ofhydroplaning and/or can result in decreased handling of the vehicle.Moreover, driving can create friction between tires and the road, andtire treads can function to help cool the tires, reducing the effects ofthe heat caused by driving. Low-tread tires can reduce the ability ofthe tire to cool, resulting in the heat experienced by the tires toreach unsafe levels. This can ultimately result in a blowout, whichcould cause a driver to lose control of a vehicle, especially whiletraveling at high speeds.

In addition, low-tread tires generally retain air less efficiently thantires with sufficient tread depth. Thus, low-tread tires can be moresusceptible to becoming low-pressure tires. Improperly inflated tiresare typically unable to properly grip the road, regardless of roadconditions, making it more difficult for a driver to steer the vehicle.Improperly inflated tires can also cause a vehicle to skid during suddenstops, can reduce gas mileage of a vehicle, and/or can cause the tiretread to wear more quickly. As another example, low-tread tires can bemore susceptible blowouts after suffering a puncture as the tire nolonger have sufficient material to resist a blowout (e.g., resistshearing of the tire caused by the internal pressure of the tire) whenthe tire experiences a puncture.

Existing tires and related systems can include pressure sensors that canprovide information regarding the pressure of the tire, but there is aneed to track the tread depth of a tire, as well as other informationthat can be pertinent to the health of a tire.

SUMMARY

These and other problems can be addressed by the technology disclosedherein, which includes a system configured to monitor the health of atire. The system can include an inertial measurement unit (IMU). The IMUcan be adhered or attached within a tire and/or to a wheel (e.g., a hub)and can measure linear accelerations and angular velocities associatedwith the wheel. The system can analyze the data measured by the IMU todetermine various measures of tire health. For example, the system candetermine an estimated tread depth of the tire, as well as qualitiesassociated with the contact patch, toe, and/or camber of the tire and/orcorresponding wheel. The system can provide alerts to a computing device(e.g., a user's mobile device) indicating various qualities associatedwith the tire and/or vehicle, such as a measured use of the tire (e.g.,service time, distance traveled), a determined health of the tire,and/or various measurements, metrics, or calculations associated withthe tire.

The disclosed technology includes a tire monitoring system that cancomprise a tire sensor mounted within a tire and a computing device incommunication with the tire sensor. The computing device can beconfigured to receive kinematic sensor data from the tire sensor anddetermine a contact patch angle based at least in part on the kinematicsensor data. The kinematic sensor data can be indicative of motion ofthe tire, and the contact patch angle being an angle that represents acontact patch associated with the tire. The computing device can beconfigured to determine an estimated tread depth of the tire based atleast in part on the contact patch angle and, responsive to determiningthat the estimated tread depth of the tire is a below a tread depththreshold, output instructions to a user device associated with the tiremonitoring system. The instructions can instruct the user device toprovide an indication for one or more suggested actions.

The tire sensor can be attached to an inner liner of the tire.

The tire sensor can be attached to a wheel hub associated with the tire.

The tire monitoring system can be configured such that determining thecontact patch angle can include determining when the tire sensor entersthe contact patch and when the tire sensor exits the contact patch.

The tire monitoring system can be configured such that (i) determiningwhen the tire sensor enters the contact patch includes determining afirst time or an entry angle associated with the tire sensortransitioning from an arc-like path to a cord-like path and (ii)determining when the tire sensor exits the contact patch comprisesdetermining a second time or an exit angle associated with the tiresensor transitioning from the cord-like path to the arc-like path.

The tire monitoring system can be configured such that (i) determiningwhen the tire sensor enters the contact patch comprises determining afirst time or an entry angle associated with the kinematic sensor datapassing a first kinematic data threshold and (ii) determining when thetire sensor exits the contact patch comprises determining a second timeor an exit angle associated with the kinematic sensor data passing asecond kinematic data threshold.

The computing device can be configured to receive tire data indicativeof a model of the tire.

The one or more suggested actions can include instructions to rotate thetire with other tires of a vehicle associated with the tire,instructions to align the tire and the other tires, instructions toinflate the tire, and/or instructions to replace the tire.

The monitoring system of claim 1, wherein the computing device isconfigured to determine the estimated tread depth only during periods inwhich the contact patch angle remains approximately constant duringsuccessive rotations of the tire.

The tire monitoring system can include a pressure sensor mounted insidethe tire, and the pressure sensor can be configured to measure apressure of the tire. The pressure sensor can be in communication withthe computing device, and the computing device can be configured toreceive, from the pressure sensor, pressure data that is indicative ofthe pressure of the tire and determine the estimated tread depth of thetire based at least in part on the contact patch angle and the pressuredata.

The disclosed technology includes a method that can include receivingkinematic sensor data from a tire sensor, and the kinematic sensor datacan be indicative of motion of a tire associated with the tire sensor.The method can include determining, based on the kinematic sensor data,a contact patch size associated with a contact patch of the tire and/ordetermining, based on the kinematic sensor data, a rotation rate of thetire. The method can include determining an estimated tread depth of thetire based at least in part on the contact patch size and/or therotation rate and, responsive to determining that the estimated treaddepth of the tire is a below a tread depth threshold, outputtinginstructions to a user device associated with the tire. The instructionscan instruct the user device to provide an indication for one or moresuggested actions.

Determining the contact patch size can include determining a contactpatch angle that is indicative of an angular distance between entry ofthe tire sensor into the contact patch and exit of the tire sensor outof the contact patch. The angular distance can be calculated withrespect to a center of the tire.

The method can include determining the estimated tread depth only duringperiods in which the contact patch angle remains approximately constantduring successive rotations of the tire.

Determining the rotation rate of the tire can include calculating, basedon the kinematic sensor data, a peak angular velocity and a mean angularvelocity and calculating a peak tire rotation rate ratio by dividing thepeak angular velocity by the mean angular velocity.

Calculating the peak angular velocity can include extracting a pluralityof peak angular velocities for each of a plurality rotations of the tireand averaging the plurality of peak angular velocities, and calculatingthe mean angular velocity can include extracting a plurality of meanangular velocities for each of the plurality rotations of the tire andaveraging the plurality of mean angular velocities.

The method can include receiving pressure data from pressure sensor anddetermining the estimated tread depth of the tire based at least in parton the contact patch size and the pressure data. The pressure data canbe indicative of a pressure of the tire.

The disclosed technology includes a non-transitory, computer-readablemedium storing instructions that, when executed by one or moreprocessors, can cause a system to receive kinematic sensor data from atire sensor. The kinematic sensor data can be indicative of motion of atire associated with the tire sensor. The instructions, when executed byone or more processors, can cause the system to determine a rotationrate of the tire based on the kinematic sensor data, determine anestimated tread depth of the tire based at least in part on the rotationrate, and, responsive to determining that the estimated tread depth ofthe tire is a below a tread depth threshold, output instructions to auser device associated with the tire. The instructions can instruct theuser device to provide an indication for one or more suggested actions.

Determining the rotation rate of the tire can include (i) calculating,based on the kinematic sensor data, a peak angular velocity and a meanangular velocity associated with the motion of the tire and (ii)calculate a peak tire rotation rate ratio by dividing the peak angularvelocity by the mean angular velocity.

Calculating the peak angular velocity can include extracting a pluralityof peak angular velocities for each of a plurality rotations of the tireand averaging the plurality of peak angular velocities, and calculatingthe mean angular velocity can include extracting a plurality of meanangular velocities for each of the plurality rotations of the tire andaveraging the plurality of mean angular velocities.

Determining the contact patch size can include determining a contactpatch angle based at least in part on when the tire sensor enters thecontact patch and when the tire sensor exits the contact patch.

BRIEF DESCRIPTION OF THE FIGURES

Reference will now be made to the accompanying figures, which are notnecessarily drawn to scale, and wherein:

FIG. 1 illustrates a kinematic model of round and rigid tire, accordingto the disclosed technology;

FIG. 2 illustrates a component diagram of an example computing device,according to the disclosed technology;

FIG. 3 illustrates a kinematic model of round and flexible tire thatincludes a contact patch, according to the disclosed technology;

FIG. 4 illustrates a kinematic model of round and flexible tire thatincludes a contact patch, according to the disclosed technology;

FIG. 5 illustrates a graph depicting example IMU data corresponding toan accelerating tire, according to the disclosed technology;

FIG. 6 illustrates a graph depicting example IMU data corresponding to acontact patch, according to the disclosed technology;

FIG. 7 illustrates a graph depicting example IMU data corresponding to acontact patch, according to the disclosed technology;

FIG. 8 illustrates graphs of three example waveforms corresponding tothree types of normalized data from an IMU that corresponds to a contactpatch from an IMU, according to the disclosed technology;

FIG. 9 illustrates a graph depicting the dependence of tread depth onthe contact patch angle θ_(p) and tire pressure, according to thedisclosed technology;

FIG. 10 illustrates a flowchart depicting an example flow of data,according to the disclosed technology;

FIG. 11 illustrates a flowchart depicting an example flow of data,according to the disclosed technology; and

FIG. 12 illustrates a flowchart depicting an example flow of data,according to the disclosed technology.

DETAILED DESCRIPTION

Throughout this disclosure, the disclosed technology is described inrelation to systems configured to monitor the health of a tire. But thedisclosed technology is not so limited. For example, the disclosedtechnology can be effective in monitoring the health of multiple tires(e.g., all tires on a single vehicle or a fleet of vehicles), as well asproviding alerts regarding when to rotate, adjust, and/or replace one ormore tires.

The disclosed technology includes a system comprising a tire-mountedand/or wheel-mounted (e.g., mounted to the hub) inertial measurementunit (IMU), which can be configured to measure linear acceleration dataand/or angular velocity data. The IMU can be configured to measurelinear acceleration data and/or angular velocity data associated withthe motion of a tire, and the system can be configured to determinevarious indicators of tire health based on the linear acceleration dataand/or angular velocity data. The system can be configured to determinea rolling radius of the tire and/or a distance between the IMU radius ofrotation and a rolling radius of the tire. The system can be configuredto monitor changes in one or both of these distances over time, whichcan be indicative of tread wear over time. Accordingly, the system canbe configured to monitor tread depth of a tire and/or monitor change inthe tread depth over time. The system can be configured to providealerts to a computing device, such as a user's mobile device, indicatinga determined health of a tire, the measured use (e.g., service time,distance traveled) of a tire, as well as other metrics, and the systemcan also be configured to suggest actions to increase the overall safetyand/or efficiency of a vehicle as it relates to a tire (e.g., rotatetires, align tires, inflate tires, replace tires). For example, thesystem can be configured to transmit one or more alerts to the user'smobile device or some other computing device.

Various aspects of the disclosed technology will be described more fullyhereinafter with reference to the accompanying drawings. This disclosedtechnology can, however, be embodied in many different forms and shouldnot be construed as limited to the embodiments set forth herein. Thecomponents described hereinafter as making up various elements of thedisclosed technology are intended to be illustrative and notrestrictive. Many suitable components that would perform the same orsimilar functions as components described herein are intended to beembraced within the scope of the disclosed electronic devices andmethods. Such other components not described herein may include, but arenot limited to, for example, components developed after development ofthe disclosed technology.

In the following description, numerous specific details are set forth.But it is to be understood that embodiments of the disclosed technologycan be practiced without these specific details. In other instances,well-known methods, structures, and techniques have not been shown indetail in order not to obscure an understanding of this description.References to “one embodiment,” “an embodiment,” “example embodiment,”“some embodiments,” “certain embodiments,” “various embodiments,” etc.,indicate that the embodiment(s) of the disclosed technology so describedcan include a particular feature, structure, or characteristic, but notevery embodiment necessarily includes the particular feature, structure,or characteristic. Further, repeated use of the phrase “in oneembodiment” does not necessarily refer to the same embodiment, althoughit can.

Throughout the specification and the claims, the following terms take atleast the meanings explicitly associated herein, unless the contextclearly dictates otherwise. The term “or” is intended to mean aninclusive “or.” Further, the terms “a,” “an,” and “the” are intended tomean one or more unless specified otherwise or clear from the context tobe directed to a singular form.

Unless otherwise specified, the use of the ordinal adjectives “first,”“second,” “third,” etc., to describe a common object, merely indicatethat different instances of like objects are being referred to, and arenot intended to imply that the objects so described should be in a givensequence, either temporally, spatially, in ranking, or in any othermanner.

The disclosed technology relates to a system for monitoring the healthof a tire. The system can include an IMU adhered (e.g., by tape, glue,epoxy, or something other adhesive) or otherwise attached within a tireand/or to a wheel. For example, the IMU can be adhered to the innerliner of a tire, the wheel rim, or the wheel hub. The IMU can beconfigured to detect and measure inertial data. The IMU can beconfigured to detect and measure linear accelerations and angularvelocities associated with the tire in which the IMU is mounted. Thesystem can be configured to determine, based at least in part on thelinear acceleration data and the angular velocity data, changes in thedistance between the IMU and the outer rolling surface. As will beappreciated, the difference in distance between the IMU and the outerrolling surface of the tire will decrease with tread wear (i.e., as thetread depth of the tire decreases). Accordingly, the system can beconfigured to monitor change in the tread depth over time. The systemcan be configured to measure other data, quantities, and aspectsassociated with the tire. Various aspects and functionalities of thedisclosed technology are discussed more fully below.

FIG. 1 is a kinematic model of a system 100 including a theoretical,perfectly round tire 102 that rolls without slipping. The system 100 caninclude an IMU 104 mounted in the tire 102. The system 100 can include acomputing device. Alternately or in addition, the computing device 200can be separate from the system 100, and the system 100 can beconfigured to communicate with the computing device 200 (e.g., the IMU104 can be configured to transmit detected data to an external computingdevice). As will be appreciated, the computing device 200 can refer to acomputing device co-located with and/or integrated into the IMU 104,disposed on the vehicle to which the tire 102 is attached, a remoteserver or other computing device, a user device (e.g., a mobile phone,tablet, laptop), any other computing device capable of performing one ormore of the functionalities disclosed herein, and/or any combinationthereof. For example, any of the aforementioned computing devices can beconfigured to perform some or all calculations or processing associatedwith the disclosed technology or multiple of the aforementionedcomputing devices can be configured to cooperate perform at least somecalculations in various divisions and orders of steps.

An example computing device 200 configured to implement the system 100is shown in more detail in FIG. 2. As shown, the computing device 200can include a controller 210 (e.g., a processor); an input/output (I/O)device 220; a memory 230, which can contain an operating system (OS)232, a storage device 234, which can be any suitable repository of dataand which can include a memory module and a program 236; and acommunication interface 240. The communication interface 240 can includea transceiver. The controller 210 can be in communication with the IMU104, such as wireless communication, and the controller 210 can beconfigured to receive data from the IMU 104 and determine various tirehealth attributes and values based at least in part on the data receivedfrom the IMU 104.

The controller 210 can include one or more of an application specificintegrated circuit (ASIC), programmable logic device, microprocessor,microcontroller, digital signal processor, co-processor or the like orcombinations thereof capable of executing stored instructions andoperating upon stored data. The memory can include one or more suitabletypes of memory (e.g., volatile or non-volatile memory, random accessmemory (RAM), read only memory (ROM), programmable read-only memory(PROM), erasable programmable read-only memory (EPROM), electricallyerasable programmable read-only memory (EEPROM), magnetic disks, opticaldisks, floppy disks, hard disks, removable cartridges, flash memory, aredundant array of independent disks (RAID), and the like) for storingfiles including operating system, application programs (including, forexample, a web browser application, a widget or gadget engine, and orother applications, as necessary), executable instructions and data. Thecontroller 210 can include a secure microcontroller, which can beconfigured to transmit and/or facilitate secure lines of communication.As will be appreciated, some or all of the processing techniquesdescribed herein can be implemented as a combination of executableinstructions and data within the memory.

The controller 210 can be one or more known processing devices, such asa microprocessor from the Pentium™ family manufactured by Intel™, theTurion™ family manufactured by AMDυ, or the Cortex™ family or SecurCore™manufactured by ARIVI™. The controller 210 can constitute a single-coreor multiple-core processor that executes parallel processessimultaneously. For example, the controller 210 can be a single coreprocessor that is configured with virtual processing technologies. Thecontroller 210 can use logical processors to simultaneously execute andcontrol multiple processes. The controller 210 can implement virtualmachine technologies, or other similar known technologies to provide theability to execute, control, run, manipulate, store, etc. multiplesoftware processes, applications, programs, etc. One of ordinary skillin the art would understand that other types of processor arrangementscould be implemented that provide for the capabilities disclosed herein.

The computing device 200 can include one or more storage devices 234configured to store information used by a controller 210 (or othercomponents) to perform certain functions related to the disclosedtechnology. As an example, the computing device 200 can include memory230 that includes instructions to enable controller 210 to execute oneor more applications, network communication processes, and any othertype of application or software known to be available on computersystems. Alternatively, the instructions, application programs, etc. canbe stored in an external storage or available from a memory over anetwork. The one or more storage devices can be a volatile ornon-volatile, magnetic, semiconductor, tape, optical, removable,non-removable, or other type of storage device or tangiblecomputer-readable medium.

The computing device 200 can include memory 230 that includesinstructions that, when executed by the controller 210, cause thecomputing device 200 to perform one or more processes consistent withthe functionalities disclosed herein. Methods, systems, and articles ofmanufacture consistent with the disclosed technology are not limited toseparate programs or computers configured to perform dedicated tasks.

The memory 230 can include one or more memory devices that store dataand instructions used to perform one or more features of the disclosedtechnology. The memory 230 can also include any combination of one ormore databases controlled by memory controller devices (e.g., one ormore servers, etc.) or software, such as document management systems,Microsoft™ SQL databases, SharePoint™ databases, Oracle™ databases,Sybase databases, or other relational databases. The memory 230 caninclude software components that, when executed by the controller 210,cause the computing device 200 to perform one or more processesconsistent with the disclosed technology. The memory 230 can include amemory module consistent with the disclosed technology.

The computing device 200 can also be communicatively connected to one ormore memory devices (e.g., databases (not shown)) locally or through anetwork. The remote memory devices can be configured to storeinformation and can be accessed and/or managed by the computing device200. By way of example, the remote memory devices can be documentmanagement systems, Microsoft™ SQL database, SharePoint™ databases,Oracle™ databases, Sybase™ databases, or other relational databases.Systems and methods consistent with disclosed technology, however, arenot limited to separate databases or even to the use of a database.

The computing device 200 can include any number of hardware and/orsoftware applications that are executed to facilitate any of theoperations. The one or more I/O interfaces can be utilized to receive orcollect data and/or user instructions from a wide variety of inputdevices. Received data can be processed by one or more computerprocessors as desired in various implementations of the disclosedtechnology and/or stored in one or more memory devices.

As will be appreciated, the IMU 104 can be mounted at a position havinga radius ρ within the perfectly circular tire 102 of outer radius rrolling at angular speed {dot over (θ)}(t). The IMU 104 can experience acentripetal acceleration by virtue of the IMU 104 rotating within thetire 102 at angular speed {circumflex over (θ)}(t) at radius ρ. If thetire 102 rolls with rotational velocity {dot over (θ)}(t) andaccelerates with rotational acceleration {umlaut over (θ)}(t), the IMU104 can also experience a linear acceleration associated with theforward acceleration a_(roll) of the tire 102. If the tire 102 slipsnegligibly against the road or ground as it rolls, thena_(roll)=r{umlaut over (θ)}(t). As will be appreciated, the amplitude ofthe linear acceleration can be sinusoidally modulated as the IMU 104rotates in and out of alignment with the forward motion of the tire 102(in instances where the tire 102 is traveling forward) along the ground.

Accordingly, the system 100 can be configured to determine a “rollingradius” of the tire 102 based on the dynamics of an accelerating tire102. That is, for an accelerating tire 102, the system 100 can sense theouter radius r based, at least in part, on the detected translationaland rotational accelerations, and based on the principle that the radiusr of the tire 102 will decrease as the tire 102 wears and tread depthdecreases, the system 100 can determine the tread depth of the tire 102.To determine the tread depth value, the system 100 can compute the ratioof the translational and rotational accelerations to determine theradius r of the tire 102 at any time t. Alternatively, the system 100can integrate the detected accelerations over some time interval (e.g.,some predetermined time interval, some random time interval) todetermine changes in translational velocity and rotational velocity andcan determine a ratio of the translational and rotational velocities.Alternatively, the system 100 can twice integrate the accelerations toobtain translational and rotational displacements and can determine aratio of the translational and rotational velocities:

$\begin{matrix}{r = {\frac{a_{roll}\left( t_{1} \right)}{\overset{¨}{\theta}\left( t_{1} \right)} = {\frac{\int_{t_{1}}^{t_{2}}{{dt}^{\prime}{a_{roll}\left( t^{\prime} \right)}}}{{\overset{.}{\theta}\left( t_{2} \right)} - {\overset{.}{\theta}\left( t_{1} \right)}} = \frac{\int_{t_{1}}^{t_{2}}{{dt}^{\prime}{\int_{t_{1}}^{t^{\prime}}{{dt}^{''}{a_{roll}\left( t^{''} \right)}}}}}{{\theta \left( t_{2} \right)} - {\theta \left( t_{1} \right)}}}}} & (1)\end{matrix}$

While the IMU 104 may not measure a_(roll)(t) directly, one of skill inthe art will understand that the system 100 can be configured to derivethis value from the accelerations that the IMU 104 does directlymeasure, namely a_(r)(t) and a_(θ)(t). For example, the system 100 canbe configured to determine a_(roll)(t) using Equation 2 or Equation 3:

$\begin{matrix}{{a_{roll}(t)} = \frac{{a_{\theta}(t)} - {\rho {\overset{.}{\theta}(t)}^{2}} - {g\mspace{11mu} \cos \mspace{11mu} {\theta (t)}}}{\sin \mspace{11mu} \theta \mspace{11mu} (t)}} & (2) \\{{a_{roll}(t)} = \frac{{a_{r}(t)} + {\rho {\overset{¨}{\theta}(t)}} + {g\mspace{11mu} \sin \mspace{11mu} {\theta (t)}}}{\cos \mspace{11mu} {\theta (t)}}} & (3)\end{matrix}$

where g is the acceleration due to gravity. As will be appreciated, thethree ratios shown in Equation 1 are equivalent in an idealized model(e.g., as depicted in FIG. 1), but in a realistic application in whichdata from the IMU 104 can include “noise,” one or more of Equations 1,2, and 3 can prove more practical than others. Additionally, the thirdratio shown in Equation 1 can provide an “inverse wheel odometry” thatcan be used to compute the radius r of the tire 102 from the distancethe tire 102 rolls and the angle through which the tire 102 rolls.

As will be appreciated the above computations can be appropriate for aperfectly round and rigid tire, but in the case of a perfectly round,flexible tire, the size (e.g., radius r) of the tire 102 can change withinflation pressure. Accordingly, the system 100 can be configured todetermines tread depth in a differential manner using measurementsacquired from the IMU 104. Accordingly, the system 100 can be configuredto measure the difference δ between the outer radius r of the tire 102and the IMU radius ρ:

δ=r−ρ  (4)

The IMU radius ρ is defined by the position at which the IMU 104 ismounted within the tire 102, and the IMU 104 can be mounted at anyradius ρ. For example, the IMU 104 can be mounted on the wheel hub orthe tire inner liner. The system 100 can be configured to compute theIMU radius ρ from the centripetal acceleration of the IMU 104 describedabove, for example.

To illustrate a possible method of determining δ, it can be helpful toconsider a situation in which the IMU 104 is at its highest point (i.e.,directly above the center of the tire 102) such that θ(t)=2πn for someinteger n. In this case, the IMU 104 can report the accelerationcomponents shown in Equations 5 and 6:

a _(r)(t)=g−ρ{dot over (θ)} ²   (5)

and

a _(θ)(t)=(ρ+r){umlaut over (θ)}  (6)

Equation 5 indicates that the IMU's 104 radial (vertical) accelerometerregisters g in the upward direction. (Because the IMU's 104accelerometers measure the force necessary to keep a small proof massstationary with respect to the IMU's 104 body, the component of thetotal force measured by the IMU 104 that opposes the force of gravitypoints upward.) Because the IMU 104 is at its highest point on the tire,the instantaneous centripetal acceleration p{dot over (θ)}² registers inthe downward direction. As can be seen this result does not involve theouter radius r, but the outer radius r does appear in Equation 6.Equation 6 indicates that the IMU's 104 tangential (horizontal)accelerometer registers the sum of two terms: the first term due torotational acceleration and the second term equal to the tire'stranslational acceleration r{umlaut over (θ)}(t). Thus, for a perfectIMU 104 having no bias and no noise in its data and at an instant atwhich θ=2πn, a_(r), a_(θ), {dot over (θ)}, and {umlaut over (θ)} can besampled at that instant and Equations 5 and 6 can be used to compute:

$\begin{matrix}{{\rho = \frac{g - a_{r}}{{\overset{.}{\theta}}^{2}}}{and}} & (7) \\{r = {\frac{a_{\theta}}{\overset{¨}{\theta}} - \frac{g - a_{r}}{{\overset{.}{\theta}}^{2}}}} & (8)\end{matrix}$

Equations 7 and 8 can in turn be used tom compute the distance betweenthe IMU 104 and the outer tread surface:

$\begin{matrix}{\delta = {{r - \rho} = \left\lbrack {\frac{a_{\theta}}{\overset{¨}{\theta}} - {2\frac{g - a_{r}}{{\overset{.}{\theta}}^{2}}}} \right\rbrack_{\theta = {2\pi n}}}} & (9)\end{matrix}$

The system 100 can be configured to incorporate many IMU 104 samplesinto each measurement by, for example, basing the calculations on theoutput of a well-designed state estimator for θ and {dot over (θ)},which can help address the noise present in a realistic IMU 104.

Referring to FIG. 3, in practical use, loaded tires (e.g., tiressupporting the weight of a vehicle) experience a flattened contact patch306 such that the outer radius r and the IMU radius ρ are no longerconstants. Instead, the system 100 can be configured to compute theouter radius r and the IMU radius ρ as functions of the IMU angle θ, asthe outer radius r and the IMU radius ρ can change as the IMU 104 rollsthrough the contact patch. More specifically, the system 100 can beconfigured to assume that r(θ) and ρ(θ) are both constant everywhereoutside the contact patch 306 and that both r(θ) and ρ(θ) change withina region around θ=π. Thus, at IMU angles η outside the contact patch306:

r(θ)=r ₀   (10)

and

ρ(θ)=ρ₀   (11)

where r₀ and ρ₀ are constants.

In order for the tire 102 to take on the flattened shape of the contactpatch 306, the tread of the tire 102 must bunch up as it enters thepatch and then relax as it exits the patch. This gives rise to aneffective “rolling radius” that may not be equal to either the loadedradius r_(π) or unloaded radius r₀ of the tire.

The rolling radius of the tire 102 can be defined as the ratio of thelateral road speed of the tire 102 to the angular speed of the tire 102:

$\begin{matrix}{r_{roll} = \frac{v_{roll}}{\overset{.}{\theta}}} & (12)\end{matrix}$

As shown in FIG. 3, the rolling radius of the tire 102 can be betweenthe loaded radius r_(π) and unloaded radius r₀ of the tire 102. Asdiscussed herein, it can be advantageous to compute a difference δ(Equation 4) between the radius of the IMU 104 and the rolling radius ofthe tire 102, rather than attempting to compute the outer radius ritself, as the difference δ can be less sensitive to inflation pressure.In the case of a flattened tire 102, the system 100 can be configured tocalculate a modified differential {tilde over (δ)}=r_(roll)−ρ_(π).Because the IMU 104 does not experience meaningful centripetalacceleration as it traverses the flat contact patch 306, calculation ofρ_(π) can require the system 100 to perform additional modeling.Referring to FIG. 4 and as described in more detail below, the system100 can be configured to calculate ρ_(π) from a trigonometric analysisof the angular extent of the contact patch 306, which is itself measuredby “dead reckoning” the IMU 104 through the contact patch 306. It is tobe understood that the label of “306” shown in FIG. 3, as well as anyother figures illustrating graphical representations of IMU data,references IMU data that is indicative of the IMU 104 travelling throughthe contact patch 306, whereas the labels of “306” in FIGS. 3 and 4indicate the actual contact patch 306 itself.

Alternatively, the computing device 200 can be configured to compute thedifferential for a flattened tire as:

δ′≡r _(roll)−ρ₀   (13)

While δ′may not correspond to any physically extensive quantity at aparticular angular location (in that r_(roll) exists within the contactpatch 306 and ρ₀ exists outside the contact patch 306), monitoring thedifference between them can still provide an effective approach tooffsetting the effects of inflation pressure and vehicle loading on theindividual quantities. Alternately, the computing device 200 can beconfigured to estimate the specific differential

δ_(π) =r _(π)−ρ_(π) ≈r _(roll)−ρ_(π)  (14)

where ρ_(π)≡ρ(π), which is the IMU radius ρ when the IMU 104 is at itslowest point (i.e., directly below the center of the tire 102).

Equations 5 and 6 give components of the acceleration experienced by theIMU 104 at particular isolated time instants only. Correspondingexpressions valid for all times at which θ lies outside the contactpatch 306 and the associated transition regions are:

a _(r)(t)=r _(roll) sin θ(t){umlaut over (θ)}(t)−ρ₀{dot over (θ)}(t)² +gcos θ(t)   (15)

and

a _(θ)(t)=[r _(roll) cos θ(t)+ρ₀]{umlaut over (θ)}(t)−g sin θ(t)   (16)

While the IMU angle θ is in and immediately adjacent to the contactpatch 306, the IMU's 104 outputs may no longer reflect a_(r), a_(θ),{dot over (θ)} as depicted in FIG. 3, as there may be additionalrotation of the IMU 104 body due to the deformation of the tread.

The computing device 200 can be configured to use Equations 15, 16,and/or a suitably constructed state estimator to extract the rollingradius r_(roll) and IMU radius ρ₀ to compute the differential δ′. Asnoted above, computing δ_(π) requires additional modeling to determineρ_(π), which is not the same as ρ₀. To compute δ_(π), the computingdevice 200 can be configured to use Equations 15 and 16 and an accurateestimator for the IMU angle θ to determine the vertical accelerationa_(z) of the IMU 104 as a function of time and subsequently doubleintegrate the vertical acceleration a_(z) as the IMU 104 moves from itsapex (θ=2πn) to the point where it starts to enter the contact patch 306(and Equations 15 and 16 begin to fail). This can indicate the change inheight of the IMU 104 as it rolls around the axle, and since the heightis ρ₀+ρ_(π), the computing device 200 can be configured to determine anapproximation for ρ_(π).

Alternatively, the computing device 200 can be configured to determineρ_(π) based on the IMU's 104 outputs to detect the angle θ_(p) subtendedby the contact patch 306, and the computing device 200 can be configuredto then compute:

ρ_(π)=ρ₀ cos(θ_(p)/2)   (17)

Because all outputs from the IMU 104 ideally go to known constants whenthe IMU 104 enters the contact patch 306, the computing device 200 canbe configured to determine when the IMU 104 is in the contact patch 306.The computing device 200 can also be configured to measure {dot over(θ)}_(in) and {dot over (θ)}_(out) just before the IMU 104 enters thecontact patch 306 and just after the IMU 104 exits the contact patch306. The computing device 200 can be configured to subsequentlycalculate

θ_(p) ≈Δt({dot over (θ)}_(in)+{dot over (θ)}_(out))/2   (18)

where Δt is the time the IMU 104 spends in the contact patch 306.Alternatively or in addition, the system 100 can include a second IMU104. For example, the second IMU 104 can be positioned directly oppositethe first IMU 104 with respect to the center of the tire 102, which mayincrease or maximize the amount of useful data by ensuring that at leastone IMU 104 will always be outside the contact patch 306. This mayprovide a better estimate of {dot over (θ)}.

Equations 15 and 16 describe the acceleration components experienced byan IMU 104 that is physically aligned with the equatorial plane of atire 102 that is itself aligned with respect to the direction ofrolling. The more general situation of a misaligned IMU 104 and amisaligned tire 102 rolling in a fixed direction can be described asfollows. First, let u be a constant unit vector that points along theaxis of rotation of the tire 102 in a right-hand sense. Then,

$\begin{matrix}{u = \left\{ \begin{matrix}{{\cos \mspace{11mu} \kappa \mspace{11mu} \sin \mspace{11mu} \tau \mspace{11mu} e_{x}} + {\cos \mspace{11mu} \kappa \mspace{11mu} \cos \mspace{11mu} \tau \mspace{11mu} e_{y}} - {\sin \mspace{11mu} \kappa \mspace{11mu} e_{z}}} & {{for}\mspace{14mu} {the}\mspace{14mu} {left}\mspace{14mu} {wheel}} \\{{{- \cos}\mspace{11mu} \kappa \mspace{11mu} \sin \mspace{11mu} \tau \mspace{11mu} e_{x}} + {\cos \mspace{11mu} \kappa \mspace{11mu} \cos \mspace{11mu} \tau \mspace{11mu} e_{y}} + {\sin \mspace{11mu} \kappa \mspace{11mu} e_{z}}} & {{for}\mspace{14mu} {the}\mspace{14mu} {right}\mspace{14mu} {wheel}}\end{matrix} \right.} & (19)\end{matrix}$

where e_(x) and e_(z) are as defined in FIG. 1, and e_(y)=e_(z)×e_(x).Here κ and τ are the tire's 102 camber and toe angles, respectively,with toe defined relative to the direction of rolling rather than to thevehicle's longitudinal axis. If τ≠0, the condition of rolling withoutslipping of the tire 102 against the road surface as discussed above canno longer hold but can be replaced by a condition of rolling withnegligible azimuthal slipping, resulting in a forward tire accelerationof a_(roll)=r_(roll) sect τ {umlaut over (θ)}(t). The rotation axisvector u can be used to define a set of constant orthonormal basisvectors {tilde over (e)}_(θ), {tilde over (e)}_(u), and {tilde over(e)}_(r) aligned with the tire:

$\begin{matrix}{{\overset{˜}{e}}_{\theta} = \frac{u \times e_{z}}{{u \times e_{z}}}} & (20) \\{{\overset{˜}{e}}_{u} = u} & (21) \\{{\overset{˜}{e}}_{r} = {{\overset{˜}{e}}_{\theta} \times {\overset{˜}{e}}_{u}}} & (22)\end{matrix}$

The instantaneous displacement of the IMU 104 from its center ofrotation can now be written as R_(u)(θ(t))(ρ₀{tilde over (e)}_(r)),where R_(u)(φ) is an orthogonal matrix that rotates any vector itleft-multiplies by an angle φ in a right-handed sense about the axisdefined by u. (Thus the IMU's 104 displacement passes through the “topdead center” value ρ₀{tilde over (e)}_(r) each time θ(t) passes througha multiple of 2π.) The above definitions can be used to generalizeEquations 15 and 16 for the accelerations sensed by the IMU 104'saccelerometers to

a _(i)=[R _(u)(θ(t))A{tilde over (e)} _(i)]·[r _(roll) sec τ {umlautover (θ)}(t)+ge _(z)+ρ₀ R _(u)(θ(t)){tilde over (e)} _(r)]  (23)

where i represents θ, u, or r, and where A is a constant orthogonalmatrix that characterizes the misalignment of the IMU relative to thetire. Similarly the angular rates sensed by the IMU's gyroscopes can bewritten as

ω_(i)=[R _(u)(θ(t))G{tilde over (e)} _(i)]·u{dot over (θ)}(t)   (24)

where i represents θ, u, or r, and where G is a constant orthogonalmatrix that characterizes the misalignment of the IMU 104 relative tothe tire 102. One skilled in the art will appreciate that theaccelerations and angular rates reported by a real IMU 104 may not beexactly as predicted by Equations 23 and 24 but may includecontributions from imperfections such as bias and noise. It will also beappreciated that Equations 23 and 24 can be written in many equivalentforms, including forms chosen to be convenient for efficientcomputation.

As will be appreciated, as the tire 102 comes to a stop, the computingdevice 200 can be configured to use the temporarily constant componentsof the gravitation constant ge_(z) as measured by the IMU's 104accelerometers to determine the IMU's 104 orientation. Thus, thecomputing device 200 can then have a θ(t₀) to integrate from as the tire102 accelerates away from the stopped position. Such known-stationarystates can permit the computing device 200 to measure and calibrate outIMU biases, which may tend to be significant and may drift unpredictablyover time. The computing device 200 can be configured to reduce orminimize such errors by limiting how long measurements are taken by theIMU between bias nullings performed by the computing device 200 (e.g.,at stop points of the tire 102). Thus, the computing device can beconfigured to determine the vehicle is coming to a stop, null out anygyro biases of the IMU, determine θ(t₀) based on data from the IMU's 104accelerometers, determine the vehicle is beginning to accelerate, samplethe IMU 104 rapidly for a brief interval (e.g., one revolution of thetire), and process the results to produce a tread measurement.

As described herein, changes in the rolling radius of a tire 102 cancorrespond to changes in tread depth of the tire 102, and the pressure,temperature and/or load on the tire can affect the rolling radius of atire 102. To increase the overall accuracy of the system 100, the system100 can include one or more pressure sensors configured to detect and/ormonitor the internal pressure of the tire 102, and/or the system caninclude one or more temperature sensors configured to detect and/ormonitor the temperature of the tire 102. Alternately, the system 100 caninclude a geolocation sensor and can be configured to look up the localtemperature from, for example, a third-party weather service to estimatea temperature of the tires 102. Furthermore, as discussed herein, thedifferential approach to determining the tread depth of the tire 102 candecrease the impact of varying pressure on the tread depth calculation.

While it is currently difficult to determine vehicle load directly(e.g., weight of the vehicle, passengers, and cargo), the impact of theload variable can be overcome by aggregating IMU data and determining anestimated tread depth based on large, aggregated trends of data. Thatis, the computing device 200 can be configured to evaluate whether therolling radius is decreasing over time, which can be indicative of thetread depth decreasing over time. Furthermore, as discussed herein, thedifferential approach to determining the tread depth of the tire 102 candecrease the impact of varying vehicle load on the tread depthcalculation.

The system 100 can be configured to measure the change in tread depthover time. For example, the system 100 can be configured to measure orestimate a decrease in a tire's 102 rolling radius over time and candetermine a corresponding decrease in the tire's 102 tread depth by, forexample, applying the system and any of the methods described herein.The system 100 can be configured to receive an indication of the modelof tire installed on a vehicle so as to determine a starting tread depthof the tire 102, or the system 100 can be configured to receive one ormore measurement values associated with the starting tread depth of atire 102 installed on a vehicle. The system 100 can assign a defaulttread depth for a new tire 102 (e.g., 10/32″, 11/32″). The system 100can assign a default tread depth for a new tire 102 unless differentvalues or other information corresponding to the new tire 102 isprovided (e.g., a measured tread depth or a make/model of the tire). Astime progresses and the system 100 monitors and determines a decrease inthe tread depth of the tire, the system 100 can be configured to receiveone or more measurement inputs associated with a measured tread depth ofthe tire 102. These one or more measurement inputs can be used by thesystem 100 to validate, correct, and/or update the current tread depthof the tire 102 according to the system.

Alternately or in addition, the system 100 can be configured to measurethe actual tread depth of a tire 102 by, for example, applying thesystem and methods described herein. Such a configuration may requiremore precise measurements by the IMU 104 and/or other sensors (e.g., ascompared to determining a decrease in tread depth over time), but such aconfiguration can be configured to measure the actual tread depth of thetire 102 without requiring a starting tread depth to be inputted intothe system 100.

Alternatively or in addition, the system 100 can be configured todetermine an extent of the contact patch 306 of the tire based onmeasurements from the IMU 104. For example, the system 100 can beconfigured to determine the angular extent of the contact patch 306.

Alternatively or in addition, the computing device 200 can be configuredto detect relatively quiescent periods of time in which the an IMU 104adhered to the inner liner of the tire 102 is essentially stationaryrelative to the ground as it traverses through the contact patch 306.Specifically, the computing device can detect such periods by locatingrelatively constant values of linear accelerations and angularvelocities within the IMU measurements.

FIG. 5 shows example acceleration measurements from an IMU 104 mountedon the inner liner of a rotationally accelerating tire 102. The periodsof time during which the IMU 104 is within the contact patch 306 can bereadily apparent as the measured accelerations can abruptly revert torelatively constant values. The duration of these periods can decreaseas the tire 102 accelerates, though the angular extent of the contactpatch 306 (i.e., the fraction of the entire tire 102 rotation spanned bythe quiescent periods) can remain approximately constant.

FIG. 6 provides a more detailed view of an example traversal of thecontact patch 306 by the IMU 104, showing additional features of the IMUdata that can be used by the computing device 200 to determine theextent of the contact patch 306. The inward acceleration (az) canabruptly revert to a value of 1.0 as the centripetal accelerationassociated with following a circular trajectory ceases and the IMU 104traverses the flat contact patch 306—only the acceleration of gravitymay remain. The acceleration of the IMU 104 about an axis tangent to thetire perimeter (ax) can briefly have a value of zero within the contactpatch 306. Positive and negative spikes on the edges of the patch canindicate a circumferential compression then extension of the tire wallas it enters then exists the contact patch 306. The angular velocity ofthe IMU 104 about an axis parallel to the axle of the tire and/or wheel(ω) can generally be zero or substantially close to zero through thecontact patch 306. On either side of the zero-valued period, there canbe brief peaks of larger angular velocity as the IMU 104 abruptly “tips”into and out of the contact patch 306.

The computing device 200 can use any of several measures to quantify theextent of the contact patch 306. FIG. 7 provides a pictorialrepresentation of these measures relative to the dip in angular velocity(ω) measured by the IMU 104 as it passes through the contact patch 306.The computing device 200 can use the following definitions to enumeratethe quantities of FIG. 7:

to—time near zero (less than half mean angular velocity);

tp—time between peaks on either side of dip in angular velocity;

t20—time spent more than 20% above mean angular velocity;

t10—time spent more than 10% above mean angular velocity; and

peak—ratio of peak angular velocity to mean angular velocity.

Consistent with the methodologies described herein, the angle subtendedby the contact patch 306 at the axle associated with the tire 102 can bereferred to as the contact patch angle θ_(p) (see FIG. 3). The contactpatch angle θ_(p) can refer to the angle between the “entry” and “exit”instants t_(in) and t_(out) associated with the beginning and end of thecontact patch 306. That is, assuming a constant rotational speed, alarger difference between t_(in) and t_(out) will correspond to a largercontact patch angle θ_(p). Example entry and exit instants can includethe moments at which IMU data (e.g., angular velocity data, linearacceleration data, magnetic field strength) passes (e.g., becomesgreater than, becomes less than) a predetermined percentage of thecorresponding average IMU data or the corresponding average IMU datawhen the IMU 104 is outside the contact patch 306. Other example entryand exit instants can include the moments at which the IMU data reachesor passes predetermined maxima or minima of the IMU data that isassociated with the contact patch 306. Regardless of the threshold(s)used, a first IMU data threshold can correspond to the entry instantt_(in) and a second IMU data threshold can correspond to the exitt_(out). The first IMU data threshold can be different from the secondIMU data threshold. Alternatively, the first IMU data threshold can bethe same as the second IMU data threshold.

As an illustrative example, FIG. 7 depicts a graphical illustration ofexample entry and exit instants corresponding to gyroscopic IMU data;although entry and exit instant can be determined from accelerationdata, too. To provide the IMU data for most accurately determiningθ_(p),it can be useful to obtain and analyze gyroscope data corresponding to agyroscopic sensor (e.g., IMU 104) that is aligned with, or nearlyaligned with, the rotation axis of the tire 102 and accelerometer datacorresponding to an acceleration sensor (e.g., IMU 104) that is alignedorthogonally, or nearly orthogonally, to that axis. For example, the IMU104 can include a gyroscope with one or more gyroscope axes, anaccelerometer with two or more accelerometer axes, or a combinationthereof. The gyroscopic sensor can be the same sensor as theacceleration sensor (e.g., IMU 104), or they can be different sensors(e.g., multiple IMUs 104). That is, a single IMU 104 can include both agyroscope and an accelerometer (or any other motion measuring device);however, it is also contemplated that a first IMU 104 can include agyroscope, while a second IMU 104 can include an accelerometer.

As tread depth decreases over the life of a tire 102, certain aspectsand features of the tire 102 change, and changes in these aspects orfeatures can be used to determine or approximate the tread depth of thetire 102. The relationships between tread depth wear and changes inthese aspects or features can be specific to each tire model. Thus, atread depth estimation model can be constructed for a given tire model,and the tread depth estimation for that tire model need not be alteredor replaced unless a manufacturing change or some other change occursthat results in different deformation characteristics of the tire model.

For example, as tread depth decreases, the size and shape of the contactpatch 306 changes. More specifically, the width of the contact patch 306(which can be expressed as θ_(p)) can change as tread depth decreases.Typically, the width of the contact patch 306 will decrease as the treaddepth decreases, although for some models of tire, the width of thecontact patch 306 may increase as the tread depth decreases. Regardless,it is possible to associate changes in the width of the contact patch306 with decreases in tread depth, as discussed herein. As a relatedexample, as tread depth changes, the tilt angle, speed, and otheraspects of the tire 102 (and the liner of the tire 102) within thecontact patch 306 can also change.

Multiple methods or models can be employed to determine the contactpatch angle θ_(p). For example, the contact patch angle θ_(p) can bedetermined based on entry instant t_(in) and exit instants t_(out). Afirst method, Method 1, can include constructing a wheel rotation model(e.g., implementing some or all of Equations 15, 16, and 19-24),determining the angles θ_(in) and θ_(out) that correspond to t_(in) andt_(out), respectively, and computing the contact patch angle θ_(p) asthe contact patch exit angle θ_(out) less the contact patch entry angleθ_(in). For example, a state estimator (e.g., Kalman filter, regressionanalyzer) can be configured to determine the contact patch angle θ_(p).

Because a tire angle θ can be associated with every time instant t, theIMU data can be expressed as one or more functions of θ rather than t.This in turn allows normalized versions of multiple contact patchwaveforms (corresponding to respective types of IMU data) to be alignedwith one another and coherently averaged in order to reduce the effectsof random noise. This normalization can be performed even if thedifferent contact patch waveforms were sampled at different wheelrotation rates co. It can be useful to perform the normalizations suchthat the results are approximately independent of ω. For example, asuitable normalization for gyroscope rates can be performed by dividingthe gyroscope rate data ω. FIG. 8 depicts an example of three waveformscorresponding to three types of normalized data—ω_(y)data, a_(z) data,and a_(x)data—that are each the result of averaging approximately 40normalized IMU waveforms (from a gyroscope aligned with the tire's 102rotation axis (ω_(y) data) and from two accelerometers alignedorthogonally to that axis (a_(z) data and a_(x)data) and aligned suchthat the contact patch portions of the respective data type generallyaligns with that of the other types of data.

Another example method, Method 2, involves estimating the tire rotationrate ω by averaging tire rotation rates ω^(gyro) sampled from gyroscopedata at times (or angles) well removed from the contact patch 306 andcalculating ω(t_(out)−t_(in)) to determine the contact patch angleθ_(p). Any misalignment of the IMU 104's gyroscope axes with the tire102 can be circumvented or minimized by computing the Euclideanmagnitude of the three rate components before averaging:

$\begin{matrix}{\omega^{gyro} = \left\lbrack {\left( \omega_{1}^{gyro} \right)^{2} + \left( \omega_{2}^{gyro} \right)^{2} + \left( \omega_{3}^{gyro} \right)^{2}} \right\rbrack^{\frac{1}{2}}} & (25)\end{matrix}$

In addition or alternatively, values of θ_(p)from multiple contact patchtraversals can be averaged to reduce the effects of random noise.

Another example method, Method 3, involves estimating the rotation rateω of the tire 102 by dividing 2π radians by the average time betweensuccessive contact patches 306 and computing: θ_(p)=ω(t_(out)−t_(in)).In addition or alternatively, values of θ_(p)from multiple contact patchtraversals can be averaged to reduce the effects of random noise.

Yet another example method, Method 4, involves partitioning all IMU datainto a first group for data obtained inside contact patches (i.e.,between t_(in) and t_(out) for any contact patch 306) and a second groupfor data obtained outside contact patches over one or more completerotations (e.g., as determined using successive t_(in) instants). Thepartitioning can be performed after the data has been collected or whilesampling from the IMU 104 (e.g., receiving data from the IMU 104), andthe sampling can be performed at a constant rate. Corresponding samplecounts N_(in) and N_(out) can be used to compute θ_(p)=2πN_(in)/N_(out).It will be appreciated that Method 4 can be equivalent to Method 3 butdoes not explicitly reference time or rate values.

These and any other such methods can provide differing balances ofaccurate results and computational efficiency. For example, Method 1 cantypically produce the most accurate results, particularly underacceleration conditions of the tire 102, but Method 1 also requires themost computational power of these example methods. Methods 2, 3, and 4are typically less computationally expensive than Method 1, and Methods3 and 4 generally provide the added benefits of being insensitive toboth sample rate (assuming it is essentially constant) and IMU scalecalibration. To limit errors due to acceleration when using Methods 2through 4, it can be helpful to repeatedly measure the time interval (ornumber of samples) between successive contact patches 306 (e.g.,measuring successive t_(in) instants) and evaluate estimated tread depthonly during periods (i.e., stretches of successive contact patches 306)in which this interval stays relatively constant (e.g., below apredetermined amount of variation or deviation from an average t_(in)instant). Regardless of the method used, it can be beneficial to performlowpass filtering of IMU data before use, which can help provide moreaccurate results.

In addition or alternatively, a peak tire rotation rate ratio r_(peak)(illustrated in FIG. 7) (i.e., the ratio of peak angular velocity tomean angular velocity for at least one rotation of the tire) can be usedto determine the contact patch size. As an example, the peak tirerotation rate ration r_(peak) can be measured by extracting peak andaverage rotation rates from estimated (and perhaps coherently averaged)gyroscope waveforms generated by a state estimator of the type describedin Method 1 above. As another example, the peak tire rotation rateration r_(peak) can be measured by extracting corresponding peak andaverage rotation rates from raw or lowpass-filtered gyroscope data andaveraging over multiple contact patch traversals. As will beappreciated, any errors due to acceleration can be greatly reduced whena state estimator is used. Any such errors can be reduced, in additionor alternatively, by evaluating tread depth only during periods when theinter-patch interval remains nearly constant.

Both the contact patch angle θ_(p) and the peak tire rotation rate ratior_(peak) can typically depend on tire pressure and wheel load, inaddition to tread depth. Specifically, both of these features tend toincrease with decreasing pressure. Accordingly, it can be helpful toincorporate a pressure sensor (e.g., into the IMU sensor 104, although apressure sensor separate from the IMU sensor 104 can be used) and toinclude pressure dependence in the tire-model-specific models relatingthe contact patch angle θ_(p) and the peak tire rotation rate rationr_(peak) to tread depth changes. The outcome of the characterization foreach tire model is then a function that maps the contact patch angleθ_(p) to tread depth and/or the contact patch angle r_(peak) to treaddepth, as well as the and pressure to tread depth. For illustrativepurposes only, FIG. 9 provides a graph depicting the dependence of treaddepth on the contact patch angle θ_(p) and tire pressure (underzero-load conditions).

If wheel load is desired to be included in the model(s), load data froma load cell or another sensor configured to measure load, pressure,and/or force (e.g., as discussed more fully below) can be used.Alternatively, a backend analysis can be performed to compute (e.g., bythe system 100) nominal tread depths without regard to load and ahistory of the results can be maintained (e.g., by the system 100) suchthat historical data detailing load over time is created. Becausevehicle load, and therefore wheel or tire load, typically increases anddecreases over time within a limited range, the system 100 can analyzethe history of computed nominal tread depths to determine a long-termtrend or relationship between the computed nominal tread depths and thecorresponding real tread depth decrease. As a simple example,measurements made when a vehicle is minimally loaded typically producethe smallest nominal tread depth values (when load dependence is omittedfrom the computation), so an accurate tread depth trend can be obtainedfrom just the values at the local minima, or valleys, of the nominaltread depth history.

In addition or alternatively, load changes can be estimated byexploiting differences in the way different features like the contactpatch angle θ_(p) and the peak tire rotation rate ration r_(peak) dependon load. If their load dependences of the contact patch angle θ_(p) andthe peak tire rotation rate ration r_(peak) are sufficiently different(which is the case for at least some tire models), to the system 100 canconstruct a function or model that maps multiple feature values (e.g.,data indicative of the contact patch angle θ_(p) and/or data indicativeof the peak tire rotation rate ration r_(peak)) and pressure data to aunique tread depth.

Regardless of how load changes are accounted for over the life of a tire102, there can still be an overall load dependence due to the vehicle'sunloaded weight. That is, different types of vehicle can have differentunloaded vehicle weights (i.e., the weight of the vehicle itself), whichmay cause the sensor to produce different feature values (e.g.,acceleration, rotation rate, contact patch angle θ_(p), peak tirerotation rate ration r_(peak)) even if all vehicles have the same typeof tire and have the same amount of extra weight added to the respectivevehicles. This variation can be reduced or minimized by, at the time ofsensor installation, recording the initial tread depth (e.g., in thesystem 100). As an example, this process can be automated when sensorsare installed in new tires under the assumption that all new tires of agiven tire model will have the same initial tread depth uponinstallation (when installed as a new, previously unused tire). Theinitial tread depth can be used as a calibration point. That is, uponinstallation of a new tire 102, the IMU 104 and/or system 100 candetermine a contact patch angle of the new tire 102 and a pressure ofthe new tire 102. Based on the processes and methodologies describedherein in combination with the known tread depth and/or pressure of thenew tire 102, the IMU 104 and/or system 100 can determine the load onthe tire 102 at installation. As an example, a heavy vehicle and a lightvehicle can both have a new tire 102 of the same model installed, andeither vehicle will produce a different patch angle, which can be usedto determine information about the vehicle weight through the determinedtire load.

Referring to FIG. 10, which depicts an example flow of data for thesystem 100, the system 100 can be configured to transfer data betweenone or more sensors, the computing device 200, and/or some other devicesuch as a user device (e.g., a mobile device, a vehicle-based device)and/or a server (e.g., a third-party server, a cloud-based host). Theone or more sensors (e.g., IMU 104) can detect sensor data and transmitthe sensor data to the computing device 200. The sensor as depicted caninclude an IMU 104, temperature gauge, pressure gauge, piezoelectricflex sensors, or any other sensor, and the sensor data can include oneor more of acceleration, rotational velocity, tire flexing intensity,pressure, and temperature. The computing device 200 can be configured toestimate or otherwise determine state variables based at least in parton the sensor data. The state variables can include kinematic variables(angular position, rotation counts) not directly measured or measurableby the one or more sensors, sensor characterization parameters (e.g.,biases, sensor alignment angles, rotation counts), and tire properties(including those described above) such as tire alignment angles (e.g.,toe and camber), contact patch size, IMU radius, rolling radius, andtread depth.

The computing device 200 can be configured to estimate or determine oneor more state variables based on consecutive measurements from thesensor(s) within a predetermined amount of time or a predeterminednumber of events (e.g., a predetermined number of tire rotations). Eachstate variable update (e.g., successive sensor data) can correspond toan observation window rather than a single measurement. Successiveobservation windows can be widely separated in time. This can savepower, which is particularly useful if the sensor(s) arebattery-powered. Alternately or in addition, this can enable thecomputing device 200 to select only observation windows (e.g., sensordata corresponding to particular times, positions, or rotation angles)at which it is easier to analyze the tire motion. For example, thecomputing device 200 can be configured to select only observationwindows in which the vehicle is moving slowly but acceleratingsignificantly. As another example, the computing device can beconfigured to select only observation windows in which the sensor (e.g.,IMU 104) is moving through the contact patch 306 and/or the tire 102 isnot accelerating (i.e., the tire 102 has an acceleration (e.g.,horizontal, angular) that is zero or substantially close to zero).

As depicted in FIG. 10, the box 1002 labeled “Window Selection” canrepresent the selection of observation windows for further processing,and the computing device 200 can be configured to select one or moreobservation windows. Observation windows that are selected can beanalyzed by the computing device 200, such as for physical stateestimation. Various methods for such estimations are discussed herein(e.g., tread depth estimation). The computing device 200 then saves,locally or remotely, the estimated physical state data. The savedphysical state data can be subsequently analyzed or processed such asfor trend and/or change analysis. The further analysis (e.g., trendand/or change analysis) can be conducted by the computing device 200and/or some other device (e.g., a remote server). Regardless of whichcomputing device is being utilized, the trend analysis can identifyrates of change for slowly varying state variables, especiallyparameters corresponding to physical quantities of predeterminedinterest (e.g., wheel and/or tire alignment angles, tread depth). Thetrend analysis can include performing a lowpass filter to removemeasurement noise that survives or is created by the state estimation ofthe observation window analysis.

The system can include an outlier detection module (e.g., as denoted bybox 1004 in FIG. 10, which is labeled “Outlier Detection”), which candiscard undesired state updates. For example, these can occur when astate estimation is performed while the vehicle is in a state of motionnot well described by the underlying model. For example, the computingdevice 200 or some other device can be configured to identify relativelysudden changes in state variables that ordinarily change at a slow rate.Alignment values can change suddenly as a result of an encounter with adeep pothole or some other obstacle, for example, but tread depth willnot generally change quickly. As explained more fully below, the trendand/or change analysis can include recursive Bayesian estimation stepsor other techniques. That is, the trend and/or change analysis caninclude a distribution of belief over the possible values of eachrelevant state variables and update this distribution appropriately asnew upstream estimates are provided.

Referring to FIG. 11, which depicts another example flow of data for thesystem 100, the computing device 200 or some other device can beconfigured to perform state variable estimation on an observation window(e.g., sensor data) by, for example, using a combination of lowpassfiltering and nonlinear regression. For example, the computing device200 can generate a lowpass-filtered version of a sensor's (e.g., IMU104) detected rotational velocity, and the computing device 200 can beconfigured to generate an angular pose trajectory over the observationwindow. This trajectory can include several free parameters, such asgyroscope rate biases and gyroscope alignment angles. The computingdevice 200 can then use a physical model of a rotating sensor to predictthe acceleration vector the sensor would output if subject to thegenerated trajectory. This prediction can introduce additional freeparameters, including sensor position coordinates, accelerometeralignment angles, the tire alignment (e.g., toe and camber), the IMU'sradius, and the tire's rolling radius. Subsequently, the computingdevice 200 can be configured to apply a nonlinear regression to fit thepredicted acceleration (e.g., based on the behavior modeled in Equations23 and 24) to the observed acceleration by adjusting the freeparameters, such that the parameters that yield the best fit aredetermined to be the state estimates. The physical rotation model candepend on the sensor's rotational velocity as well as the sensor'sderivative and time integral. Lowpass filtering of the rotationalvelocity signal can be beneficial to prevent excessive noisecontamination in the derivative and the integral. A physical rotationmodel that is ideally suited for circular motion about the wheel axiscan be used even if the sensor is affixed to the tire's 102 inner linerprovided sensor values used in the regression are restricted tomeasurements made at times when the sensor is substantially removed fromthe contact patch 306.

Referring to FIG. 11, the computing device 200 can be configured toapply a separate regression-based estimation for each new observationwindow (e.g., successive sensor data). That is, the computing device 200can be configured to ignore in each regression-based estimation anyearlier estimates corresponding to previous observation windows. Such apractice can prevent previous data from unduly influencing updated data.

Alternately, referring to FIG. 12, the computing device 200 can beconfigured to use earlier estimates to inform newer estimates. Forexample, once a sharp estimate has been obtained for a slowly changingvariable (e.g., the tire's 102 rolling radius), the computing device 200can be configured to feed the earlier information into subsequentestimations. The computing device 200 can be configured to maintain adistribution over possible state values that describes its currentestimation (e.g., “belief”) about the sensor's state. For example, foreach new sensor measurement, the computing device 200 can be configuredto update the estimation distribution by evaluating the conditionalprobability that the state would have any particular value given theobserved measurement and a physical model of the sensor's motion. As anexample, when the computing device 200 determines the estimationdistribution is above a predetermined level of similarity to a Gaussiandistribution, the computing device 200 can be configured to apply aKalman filter. The feedback of prior estimations (e.g., “beliefs”) intothe updated estimation process can provide a basis for recursiveBayesian estimation.

In the event the feedback of prior estimations is incorrect anderroneously influences updated estimations (e.g., if the observationwindow occurs at a time when the vehicle's motion is not well describedby the underlying physical model), block 606, which is labeled“Retrospective Evaluation,” can represent logic applied by the computingdevice 200. The Retrospective Evaluation logic can be configured todetect bad updates (e.g., erroneous data) and prevent the bad updatesfrom contaminating the state estimator. As will be appreciated the trendand change analysis can be configured to improve the accuracy ofgenerated state variable estimates, which can improve the accuracy ofthe state estimator by feeding improved estimates into the stateestimator together with its own prior estimations.

While the preceding disclosure has focused largely on determining atread depth of the tire 102, the system 100 can be configured to providealternate functionalities. For example, the system 100 can be configuredto detect, via the IMU 104 or another sensor, the number of rotations ofthe tire 102 and/or the actual distance traveled by the tire 102. Asanother example, the system 100 can be configured to detect, via the IMU104 or another sensor, the size of the contact patch 306 of the tire 102as described in more detail above. The size of the contact patch 306 canbe indicative of the tire pressure and/or load experienced by the tire102. For example, a contact patch 306 above a predetermined size can beindicative of a low tire pressure and/or a high load being exerted onthe tire 102. Either scenario can increase wear of the tire 102 and maydecrease the useful life of the tire 102.

The system 100 can be configured to use the determined size of thecontact patch 306 to improve the accuracy of the tread wear calculation.For example, the computing device 200 can be configured to compute avehicle load based on the determined contact patch 306 size and apressure measurement of the tire 102. An estimate of the vehicle load,combined with the pressure measurement, can be used to address thedependency of rolling radius on inflation pressure and vehicle loaddescribed above.

The system 100 can be configured to more directly determine the loadexperienced by a tire 102, which can increase the accuracy of thedetermined size of the contact patch 306, which can in turn increase theaccuracy of the determined rolling radius, tread depth, and/or othermetrics. The system 100 can include one or more load sensors configuredto determine the load experienced at or near one or more tires 102. Forexample, the system 100 can include a load cell or another sensorconfigured to measure load, pressure, and/or force. The load sensor canbe installed at or near an axle, a vehicle hub, a wheel hub, or anyother location on a vehicle that can be useful for determining the loadexperienced by a tire 102. As a more specific example, one or more loadsensors can be located proximate one, some, or all of the wheel hubbolts that attach a wheel to a vehicle, which can provide detailedinformation regarding the load experienced by the corresponding tire102. The load sensor can be configured to communicate (e.g., wirelessly)with the system 100.

The system 100 can be configured to determine load indirectly via one ormore non-load sensors. For example, the system 100 can be configured todetermine, based on data from the IMU 104 (e.g., immediately upon thetire 102 accelerating from a stopped position and/or immediatelypreceding the tire 102 reaching a stopped position) the size of thecontact patch 306, and the system can be configured to determine, basedon the contact patch 306 determination and pressure data from a pressuresensor measuring air pressure of the tire 102, an estimated load of thetire 102.

Load measurements and/or determinations can provide an added measure ofsafety for the commercial trucking industry, for example, as thesetire-specific determinations can provide an indication of relativeloading. This can in turn enable customized adjustment of tire pressurefor specific hauling vehicles and/or specific tires of a given haulingvehicle based on determined load balances and tire placements.

The system 100 can be configured to detect, via the IMU 104, thealignment (e.g., toe and/or camber) of one or more tires on a vehicle.For example, the IMU 104 can be configured to provide a real-time ornear real-time determination of a sudden change in camber. If thecomputing device 200 does determine that the camber and/or toe hasundergone a sudden change, the computing device 200 can assume that thealignment of the tire has become misaligned. The system 100 can includean automatic alignment system configured to automatically return amisaligned tire (e.g., a tire with incorrect camber and/or incorrecttoe) to an aligned configuration. The automatic alignment system caninclude one or more actuators attached to the chassis, axle, wheel hub,or another component of the vehicle. The automatic alignment system canbe configured to tilt, rotate, and/or shift a wheel to return the tireto an aligned configuration. The amount of tilt, rotation, and/or shiftprovided by the automatic alignment system can be determined by theseverity of misalignment calculated or otherwise detected by thecomputing device 200. Also, the system 100 can provide dynamicadjustments in alignment to permit different characteristics that thealignment factors provide in different situations.

The system 100 can be configured to provide alerts andtire-health-related information to a user device. As discussed herein,the computing device 200 can serve as a user device. Alternately, thecomputing device 200 can be included in the system 100, and thecomputing device can be configured to transmit alerts to a user device(e.g., via a mobile network, the internet, RFID, Bluetooth, or someother communication method or functionality). Regardless, the system 100can be configured to provide alerts to a user, and the alerts can beindicative of alignment or misalignment of one or more tires (e.g., toe,camber, or caster), inflation pressure (e.g. underinflation) of one ormore tires, tread depth of one or more tires, temperature of one or moretires, tire rotation recommendations, tire life (e.g., time installed onvehicle, distance traveled), remaining tire life estimates, tirereplacement recommendations, or any other useful information. Possibleapplications of the aggregated data can include providing alerts toretailers and/or manufactures (e.g., alerts regarding performance, lifecharacteristics, and other factors regarding one or more types oftires), fleet management including maintenance or replacement of tiresand/or vehicles of a fleet of vehicles, and providing industry-wide datafor industry analysts.

While the disclosed technology has been described in connection withwhat is presently considered to be the most practical embodiments, it isto be understood that the disclosed technology is not to be limited tothe disclosed embodiments, but on the contrary, is intended to covervarious modifications and equivalent arrangements included within thescope of the appended claims. Although specific terms are employedherein, they are used in a generic and descriptive sense only and notfor purposes of limitation.

What is claimed is:
 1. A tire monitoring system comprising: a tiresensor mounted within a tire; a computing device in communication withthe tire sensor, the computing device being configured to: receivekinematic sensor data from the tire sensor, the kinematic sensor databeing indicative of motion of the tire; determine a contact patch anglebased at least in part on the kinematic sensor data, the contact patchangle being an angle that represents a contact patch associated with thetire; determine an estimated tread depth of the tire based at least inpart on the contact patch angle; and responsive to determining that theestimated tread depth of the tire is a below a tread depth threshold,output instructions to a user device associated with the tire monitoringsystem, the instructions instructing the user device to provide anindication for one or more suggested actions.
 2. The tire monitoringsystem of claim 1, wherein the tire sensor is attached to an inner linerof the tire.
 3. The tire monitoring system of claim 1, wherein the tiresensor is attached to a wheel hub associated with the tire.
 4. The tiremonitoring system of claim 1, wherein determining the contact patchangle comprises: determining when the tire sensor enters the contactpatch and when the tire sensor exits the contact patch.
 5. The tiremonitoring system of claim 4, wherein: determining when the tire sensorenters the contact patch comprises determining a first time or an entryangle associated with the tire sensor transitioning from an arc-likepath to a cord-like path; and determining when the tire sensor exits thecontact patch comprises determining a second time or an exit angleassociated with the tire sensor transitioning from the cord-like path tothe arc-like path.
 6. The tire monitoring system of claim 4, wherein:determining when the tire sensor enters the contact patch comprisesdetermining a first time or an entry angle associated with the kinematicsensor data passing a first kinematic data threshold; and determiningwhen the tire sensor exits the contact patch comprises determining asecond time or an exit angle associated with the kinematic sensor datapassing a second kinematic data threshold.
 7. The tire monitoring systemof claim 1, wherein the computing device is further configured to:receive tire data indicative of a model of the tire.
 8. The tiremonitoring system of claim 1, wherein the one or more suggested actionscomprises at least one of instructions to rotate the tire with othertires of a vehicle associated with the tire, instructions to align thetire and the other tires, instructions to inflate the tire, andinstructions to replace the tire.
 9. The tire monitoring system of claim1, wherein the computing device is configured to determine the estimatedtread depth only during periods in which the contact patch angle remainsapproximately constant during successive rotations of the tire.
 10. Thetire monitoring system of claim 1 further comprising a pressure sensormounted inside the tire and configured to measure a pressure of thetire, the pressure sensor being in communication with the computingdevice, wherein the computing device is further configured to: receivepressure data from pressure sensor, the pressure data being indicativeof the pressure of the tire; and determine the estimated tread depth ofthe tire based at least in part on the contact patch angle and thepressure data.
 11. A method comprising: receiving kinematic sensor datafrom a tire sensor, the kinematic sensor data being indicative of motionof a tire associated with the tire sensor; determining, based on thekinematic sensor data, a contact patch size associated with a contactpatch of the tire; determining, based on the kinematic sensor data, arotation rate of the tire; determining an estimated tread depth of thetire based at least in part on the contact patch size and the rotationrate; and responsive to determining that the estimated tread depth ofthe tire is a below a tread depth threshold, outputting instructions toa user device associated with the tire, the instructions instructing theuser device to provide an indication for one or more suggested actions.12. The method of claim 11, wherein determining the contact patch sizecomprises determining a contact patch angle that is indicative of anangular distance between entry of the tire sensor into the contact patchand exit of the tire sensor out of the contact patch, the angulardistance being with respect to a center of the tire.
 13. The method ofclaim 12 further comprising determining the estimated tread depth onlyduring periods in which the contact patch angle remains approximatelyconstant during successive rotations of the tire.
 14. The method ofclaim 11, wherein determining the rotation rate of the tire comprises:calculating, based on the kinematic sensor data, a peak angular velocityand a mean angular velocity; and calculating a peak tire rotation rateratio by dividing the peak angular velocity by the mean angularvelocity.
 15. The method of claim 11, wherein: calculating the peakangular velocity comprises extracting a plurality of peak angularvelocities for each of a plurality rotations of the tire and averagingthe plurality of peak angular velocities; and calculating the meanangular velocity comprises extracting a plurality of mean angularvelocities for each of the plurality rotations of the tire and averagingthe plurality of mean angular velocities.
 16. The method of claim 11further comprising: receiving pressure data from pressure sensor, thepressure data being indicative of a pressure of the tire; anddetermining the estimated tread depth of the tire based at least in parton the contact patch size and the pressure data.
 17. A non-transitory,computer-readable medium storing instructions that, when executed by oneor more processors, causes a system to: receive kinematic sensor datafrom a tire sensor, the kinematic sensor data being indicative of motionof a tire associated with the tire sensor; determine, based on thekinematic sensor data, a rotation rate of the tire; determine anestimated tread depth of the tire based at least in part on the rotationrate; and responsive to determining that the estimated tread depth ofthe tire is a below a tread depth threshold, output instructions to auser device associated with the tire, the instructions instructing theuser device to provide an indication for one or more suggested actions.18. The non-transitory, computer-readable medium of claim 17, whereindetermining the rotation rate of the tire comprises: calculating, basedon the kinematic sensor data, a peak angular velocity and a mean angularvelocity associated with the motion of the tire; and calculating a peaktire rotation rate ratio by dividing the peak angular velocity by themean angular velocity.
 19. The non-transitory, computer-readable mediumof claim 18, wherein: calculating the peak angular velocity comprisesextracting a plurality of peak angular velocities for each of aplurality rotations of the tire and averaging the plurality of peakangular velocities; and calculating the mean angular velocity comprisesextracting a plurality of mean angular velocities for each of theplurality rotations of the tire and averaging the plurality of meanangular velocities.
 20. The non-transitory, computer-readable medium ofclaim 17, wherein determining the contact patch size comprisesdetermining a contact patch angle based at least in part on when thetire sensor enters the contact patch and when the tire sensor exits thecontact patch.